and I have a lot of this problem like in image. The two line are separated but i want a continuous line. What rule should I choose in Topology Checker? I want to know all the separated line, so i can fix them.
Use the Must not have dangles rule, and if lines are always supposed to meet end to end rather than having an end just touch another line anywhere, use the Must not Intersect or Touch Interior. All line ends that do not meet another line end will appear as a topology error and with the topology tools you will have the option to snap, extend or trim dangle ends, or split lines that touch or cross other lines. Snap would work best for the line pair you showed. Where your lines actually should terminate in a dangle (such as cul-de-sacs and stubs in a road network), you can mark those dangles as an exception so they will no longer show up as a topology error.
See the topology rule illustrations and explanations in this help topic.